I taught in Paraguay, which is right next door to Argentina. I traveled to Argentina many times with my wife (also a teacher), and our daughter. I found it to be quite safe. You can get mugged at night in Buenos Aires, but as anywhere else, you need to be careful when you go out. I have heard of date-rape drugs being slipped in at clubs in alcoholic beverages, so be careful with those. Other than that, I would be pretty confident. Argentina is a very progressive nation (in some ways, more progressive than the US, more akin to Europe).

My wife and I taught in Paraguay for two years. The best schools I can think of in the southern cone of the continent would be:

CHILE
Nido de Aguilas

ARGENTINA
Lincoln Academy

URUGUAY
Uruguayan American School

BRAZIL
Graded
Escola Americana de Rio de Janeiro (EARJ)